1549380323-Statistical Mechanics Theory and Molecular Simulation

504 Classical time-dependent statistical mechanics and will resemble each other as they traverse the phase space. Inorder to see ...

Green–Kubo relations 505 force. As described in Section 13.1, a shearing force can be generated by placing the system between mo ...

506 Classical time-dependent statistical mechanics the form of eqns. (13.2.1) so that we can apply the linear response formula i ...

Green–Kubo relations 507 Pxy(x) =pxy(r,p) = 1 V ∑N i=1 [ (pi·ˆex)(pi·ˆey) mi + (ri·ˆex)(Fi·ˆey) ] . (13.3.9) The pressure-tensor ...

508 Classical time-dependent statistical mechanics (see Problem 13.8). Thus, taking the limitt→∞, an expression for the coeffici ...

Green–Kubo relations 509 Eqn. (13.3.18) indicates that the external force arises from an external potential field of the form φ( ...

510 Classical time-dependent statistical mechanics D= kT f Jx= kT f lim t→∞ 〈ux〉t. (13.3.26) The average〈ux〉t can now be evaluat ...

Green–Kubo relations 511 0 1 2 3 4 5 t (ps) 0 1 2 3 Dr 2 ( t) (Å 2 ) 0 1 2 3 4 5 t (ps) 0 10 20 30 40 50 C vv (t ) (Å 2 /ps 2 ) ...

512 Classical time-dependent statistical mechanics molecular dynamics simulations, one form might yield numerically more stable ...

Calculating time correlation functions 513 can be computed rather easily within a molecular dynamics simulation (Berne and Harp, ...

514 Classical time-dependent statistical mechanics ... λ=1 λ=2 λ=K t t t (^02) ∆t 4 ∆t t 0 2 ∆t 4 ∆t (a) (b) Fig. 13.5 Pictorial ...

Calculating time correlation functions 515 as an independent “sampling” of the correlation function because over each segment, t ...

516 Classical time-dependent statistical mechanics ̃b(ω) =√^1 2 π ∫∞ −∞ dte−iωtb(xt). (13.4.5) Now, consider the product ̃a(ω) ̃ ...

Nonequilibrium molecular dynamics 517 transformaandbinto the frequency domain, and a third one is needed to transform the produc ...

518 Classical time-dependent statistical mechanics Fig. 13.6 Left: Standard periodic boundary conditions. Right: Lees–Edwards bo ...

Nonequilibrium molecular dynamics 519 Fig. 13.7 Periodic boundary conditions under the box evolution of eqn. (13.5.1). matrixhin ...

520 Classical time-dependent statistical mechanics means that the coefficient of shear viscosityηmust be independent of the choi ...

Nonequilibrium molecular dynamics 521 iL 1 = ∑N i=1 [ pi mi · ∂ ∂ri +γyi ∂ ∂xi ] iL 2 = ∑N i=1 Fi· ∂ ∂pi iLmNHC=iLNHC−γ ∑N i=1 p ...

522 Classical time-dependent statistical mechanics pi←−pi+ ∆t 2 Fi xi←−xi+ ∆t [ pxi mi +γyi ] + ∆t^2 2 mi γpyi yi←−yi+ ∆t pyi mi ...

Nonequilibrium molecular dynamics 523 As shown in Appendix B, the application of periodic boundary conditions in a cubic box of ...